| A | B |
|---|
| Polygon | a plane figure that is formed by three or more segments called sides, such that the following are true 1.Each side intersects exactly two other sides, once at each endpoint 2.No two sides with common endpoint are collinear |
| Convex Polygons | : if no line that contains a side of the polygon contains a point in the interior of the polygon |
| Nonconvex Polygons or Concave Polygons | any polygon that is not convex. |
| Triangle | has 3 sides |
| Quadrilateral | has 4 sides |
| Pentagon | has 5 sides |
| Hexagon | has 6 sides |
| Heptagon | has 7 sides |
| Octagon | has 8 sides |
| Nonagon | has 9 sides |
| Decagon | has 10 sides |
| Dodecagon | has12 sides |
| n-gon | has n sides |
| A Diagonal | of a polygon is a segment that joins two nonconsecutive vertices |
| A polygon is equilateral if... | all its sides are congruent |
| A polygon is equiangular if... | all its interior angles are congruent |
| A polygon is regular if... | it is both equilateral and equiangular |
| Theorem 6.1 Polygon Interior Angles Theorem | The sum of the measures of the interior angles of a convex n-gon is (n-2)(180°) |
| Corollary to Theorem 6.1 | The measure of each interior angle of a regular n-gon is (sum of the interior angles/number of sides) |
| Theorem 6.2 Polygon Exterior Angles Theorem | The sum of the measures of the exterior angles, one from each vertex, of a convex polygon is 360° |
| Corollary to Theorem 6.2 | The measure of each exterior angle of a regular n-gon is 1/n (360°) |
| A parallelogram | is a quadrilateral whose opposite sides are parallel |
| Theorem 6.3 | If a quadrilateral is a parallelogram, then its opposite sides are congruent |
| Theorem 6.4 | If a quadrilateral is a parallelogram, then its opposite angles are congruent |
| Theorem 6.5 | If a quadrilateral is a parallelogram, then its consecutive angles are supplementary |
| Theorem 6.6 Diagonals of a Parallelogram- If a quadrilateral is a parallelogram, then its diagonals | If a quadrilateral is a parallelogram, then its diagonals bisect each other |
| Theorem 6.7 | If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
| Theorem 6.8 | If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
| Theorem 6.9 | If an angle of a quadrilateral is supplementary to both consecutive angles, then the quadrilateral is a parallelogram |
| Theorem 6.10 | If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram |
| Theorem 6.11 | If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram |
| Rhombus | is a parallelogram that has all four sides congruent |
| Rectangle | is a parallelogram that has four right angles |
| Square | is a parallelogram that is both a rhombus and a rectangle |
| Theorem 6.12 | A parallelogram is a rhombus if and only if its diagonals are perpendicular |
| Theorem 6.13 | A parallelogram is a rhombus if and only if its each diagonal bisects a pair of opposite angles |
| Theorem 6.14 | A parallelogram is a rectangle if and only if its diagonals are congruent |
| Theorem 6.15 | A quadrilateral is a rhombus if and only if it has four congruent sides |
| Theorem 6.16 | A quadrilateral is a rectangle if and only if it has four right angles |
